FRATERNIZATION isn’t allowed in sports – but it’s certainly not off-limits in the Senate race.

Following Sunday’s debate in the WCBS-TV studios, high-level advisers to Hillary Rodham Clinton and Rick Lazio rubbed shoulders and were actually very nice to each other.

Lazio media guru Mike Murphy – somehow sporting a Clinton campaign staff button – boomed a loud welcome to the first lady’s spokesman, Howard Wolfson, as the two men prepared to “spin” the assembled media following

the hourlong showdown.

State GOP spokesman Dan Allen and Wolfson playfully traded barbs with each other before Wolfson asked Lazio spokesman Dan McLagan if he was ever going to face off against him on New York 1.

“There’s a certain fascination with the other side because you almost never get to see it firsthand,” said one of the high-level campaign glad-handers.

“It’s like the final scene in the ‘Wizard of Oz’ when you get to see the little man behind the curtain.”

“If you write about this, everyone is going to get yelled at by Rick and Hillary,” added another fraternizer.

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First, there was the Lazio-Arafat photo. Now get ready for Hillary and … Mario Cuomo.

While it hardly has the shock value of being caught in a smiling grip-and-grin with the Palestinian leader, the Lazio camp is considering using a photo of the first lady with the former three-term Democratic governor.

Cuomo, who left office in 1995, is still highly unpopular upstate, where he is blamed by many residents for helping drive the region’s economy into the ground in the late ’80s and early ’90s.

While it’s still unclear if the photo will actually be used, Team Lazio considers it to be a dynamite negative attack on Clinton.

“That would send shivers down people’s spines,” said one Lazio ally.

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Apparently, “don’t ask, don’t tell” isn’t a policy followed by The Advocate, the gay and lesbian magazine that interviewed Hillary for its current issue.

Interviewer David Kirby asks Clinton: “The attacks on you and your husband – do you think any of it could be explained by homophobia?”

He adds: “Not just because of gays in the military, but also the whole whispering campaign against you, which nobody believes is true, but how do you feel about that personally … ?”

Clinton politely ducked the question to talk about how she and the president have tried to promote inclusiveness during their eight years in the White House.

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The Post’s Maggie Haberman reports that Clinton is conceding one point to Lazio – she’ll let him take better care of the reporters who follow him across the state.

Noting that Lazio has more than twice as much money in his campaign coffers – and ignoring the fact that media outlets actually pay for their own transportation – Clinton said little will change over the next month.

“They can continue to, you know, keep all of you very well taken care of on their bus and provide, you know, whatever comforts of home you need and make you feel that you’re well-cosseted and taken care of,” said the first lady, as reporters giggled.

“But I’m just confident that’s not gonna affect how you see this race, or how you feel about the two candidates,” she joked.

“I mean, if I could afford that, by George, you know, I’d have an ocean liner right now in Lake Erie. … It’s tough to be in a position of having to get the message out and try to take care of all of you.”

Clinton did note that bottled water is usually available on her press van.